Phase transition in an exactly solvable model of interacting bosons

Yu. M. Ivanchenko, Alexander A. Lisyansky, Alexander E. Filippov

Yu. M. Ivanchenko, Alexander A. Lisyansky, Alexander E. Filippov

Pavel Cejnar, Jan Jolie

Gian Luca Giorgi, Simone Paganelli, Fernando Galve

It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here we show how it is possible to build a model representing a spin chain interacting with bosons that is exactly solvable. The exact spectrum of the model at zero temperature and the ground-state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent a useful resource for phase transition detection since a measure of the phonon can give information about the phase of the spin system. A finite-temperature phase diagram is also given in the adiabatic regime.

Sebastian Stumper, Michael Thoss, Junichi Okamoto

An. A. OVCHINNIKOV

We propose a new exactly solvable pairing model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in the thermodynamic limit is found. The transition from the superfluid phase, with a Bose condensate and a Bogoliubov-type spectrum of excitations in the weak coupling regime, to the incompressible phase, with a gap in the excitation spectrum in the strong coupling regime, is observed.